1. Field of the Invention
The invention relates to diffusion tensor magnetic resonance imaging (DT-MRI) and, more particularly, to analyzing DT-MR signals using statistical properties of the diffusion tensor.
2. Background of the Invention
For the convenience of the reader, the following references describing the background of the invention are listed and incorporated herein by reference. Hereinafter, citations to the references are made by referring to the reference numeral.
The first demonstration of the measurement of the diffusion tensor from seven or more diffusion weighted echoes and the presentation of the formulas relating the diffusion weighted signal and the diffusion tensor via the b-matrix are presented in:                (1) P. J. Basser, J. Mattiello, D. LeBihan. Diagonal and off-diagonal components of the self-diffusion tensor: their relation to and estimation from the NMR spin-echo signal. 11th Annual Meeting of the SMRM, Berlin, 1992, p. 1222.        
The first demonstration of the measurement of the eigenvalues and eigenvectors of the diffusion tensor and the interpretation as their principal diffusivities and principal directions, as well as measures of diffusion anisotropy and notion of rotational invariance, are presented in:                (2) P. J. Basser, D. LeBihan. Fiber orientation mapping in an anisotropic medium with NMR diffusion spectroscopy. 11th Annual Meeting of the SMRM, Berlin, 1992, p. 1221.        
The first article describing the calculation of the diffusion weighting factors needed to calculate the diffusion tensor from the measured diffusion weighted images is:                (3) J. Mattiello, P. J. Basser, D. LeBihan. Analytical expression for the b matrix in NMR diffusion imaging and spectroscopy. J. Magn. Reson. A 108, 131-141 (1994).        
The first abstract describing the calculation of the diffusion weighting factors needed to calculate the diffusion tensor from the measured diffusion weighted images is:                (4) J. Mattiello, P. J. Basser, D. LeBihan. Analytical expressions for the gradient b-factor in NMR diffusion imaging. 12th Annual Meeting of the SMRM, New York, 1993, p. 1049.        
The following abstracts describe diffusion tensor magnetic resonance imaging:                (5) P. J. Basser, J. Mattiello, D. LeBihan. MR imaging of fiber-tract direction and diffusion in anisotropic tissues. 12th Annual Meeting of the SMRM, New York, 1993, p. 1403.        (6) P. J. Basser, J. Mattiello, R. Turner, D. L. Bihan. Diffusion tensor echo-planar imaging of human brain. 12th Annual Meeting of the SMRM, New York, 1993, p. 1404.        
The following abstract describes the b-matrix formalism for DT-MRI:                (7) J. Mattiello, P. J. Basser, D. LeBihan. Analytical expressions for the b-matrix in diffusion tensor MR imaging. SMRM Workshop: Functional MRI of the Brain, Arlington, Va., 1993, p. 223.        
The first public demonstration of DT-MRI is in:                (8) D. Le Bihan, P. J. Basser, J. Mattiello. C. A. Cuenod, S. Posse, R. Turner. Assessment of NMR diffusion measurements in biological systems: effects of microdynamics and microstructure. Syllabus for: SMRM Workshop: Functional MRI of the Brain, Arlington, Va., 1993, p. 19-26.        (9) P. J. Basser, J. Mattiello, R. Turner, D. L. Bihan. Diffusion tensor echo-planar imaging (DTEPI) of human brain. SMRM Workshop: Functional MRI of the Brain, Arlington, Va., 1993, p. 224.        
The following describe methodological issues in DT-MRI:                (10) D. Le Bihan, P. J. Basser. Molecular diffusion and nuclear magnetic resonance. In: Le Bihan D. ed. Diffusion and Perfusion Magnetic Resonance Imaging, New York: Raven Press, 1995:5-17.        (11) P. J. Basser, D. LeBihan, J. Mattiello. Anisotropic diffusion: MR diffusion tensor imaging. In: LeBihan D. ed. Diffusion and Perfusion Magnetic Resonance Imaging, New York: Raven Press, 1995:140-149.        (12) J. Mattiello, P. J. Basser, D. LeBihan. Analytical calculation of the b matrix in diffusion imaging. In: LeBihan D. ed. Diffusion and Perfusion Magnetic Resonance Imaging, New York: Raven Press, 1995:77-90.        (13) J. Mattiello, P. Basser, D. Le Bihan. The b matrix in diffusion tensor echo-planar imaging. Magn Reson Med 37, 2, 292-300 (1997).        
The following discusses a demonstration of DT-MRI measurement of anisotropy in a monkey brain:                (14) C. Pierpaoli, J. Mattiello, D. Le Bihan, G. Di Chiro, P. J. Basser. Diffusion tensor imaging of brain white matter anisotropy. 13th Annual Meeting of the SMRM, San Francisco, 1994, p. 1038.        (15) I. Linfante, T. N. Chase, P. J. Basser, C. Pierpaoli. Diffusion tensor brain imaging of MPTP-lesioned monkeys. 1994 Annual Meeting, Society for Neuroscience, Miami, Fla., 1994.        
The method to use DT-MRI to calibrate diffusion gradients is presented in:                (16) P. J. Basser. A sensitive method to calibrate magnetic field gradients using the diffusion tensor. Third Meeting of the SMR, Nice, France, 1995, p. 308.        
The first article describing the estimation of the diffusion tensor from the diffusion weighed signals or echoes are:                (17) P. J. Basser, J. Mattiello, D. Le Bihan. Estimation of the effective self-diffusion tensor from the NMR spin echo. J. Magn. Reson. B 103, 3, 247-254 (1994).        
A description of MRI stains useful in tissue characterization is discussed in:                (18) P. Basser, C. Pierpaoli. Elucidation Tissue Structure by Diffusion Tensor MRI. SMR/ESMRMB, Nice, France, 1995, p. 900.        
Novel sequences to perform fast and high-resolution DT-NIRI are presented in:                (19) P. Jezzard, C. Pierpaoli. Diffusion mapping using interleaved Spin Echo and STEAM EPI with navigator echo correction. SMR/ESMRMB Joint Meeting, Nice, 1995, p. 903.        
A demonstration of DT-MRI of the brain of a human subject is provided in:                (20) C. Pierpaoli, P. Jezzard, P. J. Basser. High-resolution diffusion tensor imaging of the human brain. SMR/ESMRMB Joint Meeting, Nice, 1995, p. 899.        (21) P. Jezzard, C. Pierpaoli. Dual-Echo Navigator Approach to Minimization of Eddy Current and Motion Artifacts in Echo-Planar Diffusion Imaging. Proceedings of the ISMRM, New York, 1996, p. 189.        
A method to use DT-MRI in transport and drug delivery applications is presented in:                (22) P. G. McQueen, A. J. Jin, C. Pierpaoli, P. J. Basser. A Finite Element Model of Molecular Diffusion in Brain Incorporating in vivo Diffusion Tensor MRI Data. Proceedings of the ISMRM, New York, 1996, p. 193.        (23) C. Pierpaoli, B. Choi, P. Jezzard, P. J. Basser, G. Di Chiro. Significant changes in brain water diffusivity obsessed under hyperosmolar conditions. SMR/ESMRMB, Nice, France, 1995, p. 31.        
DT-MRI in an animal model of cerebral ischemia is presented in:                (24) C. Pierpaoli, C. Baratti, P. Jezzard. Fast Tensor Imaging of Water Diffusion Changes in Gray and White Matter Following Cardiac Arrest in Cats. Proceedings of the ISMRM, New York, 1996, p. 314.        
The first demonstration of secondary degeneration of nerve fibers in vivo following stroke is presented in:                (25) C. Pierpaoli, A. Barnett, L. Penix, T. De Graba, P. J. Basser, G. Di Chiro. Identification of Fiber Degeneration and Organized Gliosis in Stroke Patients by Diffusion Tensor MRI. Proceedings of the ISMRM, New York, 1996, p. 563.        
Measures of diffusion anisotropy are proposed in:                (26) C. Pierpaoli, P. J. Basser. New Invariant “Lattice” Index Achieves Significant Noise Reduction in Measuring Diffusion Anisotropy. Proceedings of the ISMRM, New York, 1996, p. 1326.        
The use of hierarchical statistical estimation model to improve estimate of diffusion tensor is presented in:                (27) P. J. Basser. Testing for and exploiting microstructural symmetry to characterize tissues via diffusion tensor MRI. ISMRM, New York, 1996, p. 1323.        
The following is an issued patent for DT-MRI:                (28) P. J. Basser, J. Mattiello, D. LeBihan. Method and System for Measuring the Diffusion Tensor and for Diffusion Tensor Imaging. U.S. Pat. No. 5,539,310, issued Jul. 23, 1996.        
The application of DT-MRI to developmental biology is presented in:                (29) C. Barnett, A. Barnett, C. Pierpaoli. Comparative MRI Study of Brain Maturation using T1, T2, and the Diffusion Tensor. 5th ISMRM, Vancouver, 1997, p. 504.        
A proof that at least seven diffusion weighted images are required to characterize diffusion anisotropy fully is described in:                (30) P. J. Basser, R. Shrager. Anisotropically-weighted MRI. ISMRM Fifth Scientific Meeting, Vancouver, 1997, p. 226.        (31) R. I. Shrager, P. J. Basser. Anisotropically weighted MRI. Magn Reson Med 40, 1, 160-165 (1998).        
Perturbation analysis of errors in fiber direction and eigenvalues is presented in:                (32) P. J. Basser. Quantifying Errors in Fiber Direction and Diffusion Tensor Field Maps Resulting from MR Noise. 5th Scientific Meeting of the ISMRM, Vancouver, 1997, p. 1740.        
Simplified method for measuring diffusion tensor is presented in:                (33) P. J. Basser, C. Pierpaoli. Analytic Expressions for the Diffusion Tensor Elements. 5th Annual ISMRM, Vancouver, 1997, p. 1738.        (34) P. J. Basser, C. Pierpaoli. A simplified method to measure the diffusion tensor from seven MR images. Magn Reson Med 39, 6, 928-934 (1998).        
A proposed method for estimating eigenvalues of the diffusion tensor is given in:                (35) P. J. Basser, C. Pierpaoli. Estimating the Principal Diffusivities (Eigenvalues) of the Effective Diffusion Tensor. 5th ISMRM, Vancouver, 1997, p. 1739.        
A demonstration of DT-MRI to diagnose Pelizaeus-Merzbacher Disease is given in:                (36) C. Pierpaoli, B. Choi, R. Schiffmann, G. DiChiro. Diffusion Tensor MRI in Pelizaeus-Merzbacher Disease. 5th ISMRM, Vancouver, 1997, p. 664.        
Color mapping of fiber direction obtained from DT-MRI data is presented in:                (37) C. Pierpaoli, Oh No! One More Method for Color Mapping of Fiber Tract Direction Using Diffusion MR Imaging Data. 5th ISMRM, Vancouver, 1997, p. 1741.        
A scheme for following nerve fiber tracts using DT-MRI is presented in:                (38) P. J. Basser. Fiber-Tractography via Diffusion Tensor MRI (DT-MRJ). 6th ISMRM, 1998, p. 1226.        (39) P. J. Basser. New histological and physiological stains derived from diffusion-tensor MR images. Ann N Y Acad Sci 820, 123-138 (1997).        
The Monte Carlo method of simulating diffusion tensor MRI data is presented in:                (40) C. Pierpaoli, P. J. Basser. Toward a quantitative assessment of diffusion anisotropy. Magn Reson Med 36, 6, 893-906 (1996). Published erratum appears in Magn Reson Med 1997 June;37(6):972.        
The first paper describing DT-MPI in normal human subjects is presented in:                (41) C. Pierpaoli, P. Jezzard, P. J. Basser, A. Barnett, G. Di Chiro. Diffusion tensor MR imagine of the human brain. Radiology 201, 3, 637-648 (1996).        
Anisotropy and organization measures of diffusion is presented in:                (42) P. J. Basser, C. Pierpaoli. Microstructural and physiological features of tissues elucidated by quantitative-diffusion-tensor MRI. J Magn Reson B 111, 3, 209-219 (1996).        
Summary of diffusion tensor MRI “stains” is presented in:                (43) P. J. Basser. Inferring microstructural features and the physiological state of tissues from diffusion-weighted images. NMR Biomed 8, 7-8, 333-344 (1995).        
The first paper describing DT-MRI is:                (44) P. J. Basser, J. Mattiello, D. LeBihan. MR diffusion tensor spectroscopy and imaging. Biophys J 66, 1, 259-267 (1994).        
Applying gradient patterns for DT-MRI is discussed in:                (45) T. L. Davis, v. J. Wedeen, R. M. Weisskoff, B. R. Rosen. White matter tract visualization by echo-planar MRI. SMRM Twelfth Annual Meeting, New York, N.Y., 1993, p. 289.        
A description of nuclear magnetic resonance (NMR) noise is provided in:                (46) H. Gudbjartsson, S. Patz. The Rician distribution of noisy MRI data [published erratum appears in Magn Reson Med 1996 August;36(2):331]. Magn Reson Med 34, 6, 910-914 (1995).        (47) R. M. Henkelman. Measurement of signal intensities in the presence of noise in MR images. Med. Phys. 12, 2, 232-233 (1985).        
Bootstrap methods are discussed in:                (48) Efron B. “Bootstrap methods: Another look at the jackknife”. Ann. Statist., Vol 7, pp 1-26.        
Some statistical issues associated with interpreting DT-MRI data are discussed in:                (49) S. Pajevic, and P. J. Basser. Parametric Description of Noise in Diffusion Tensor MRI. 8th Annual Meeting of the ISMRM, Philadelphia, 1787 (1999).        (50) S. Pajevic, and P. J. Basser. Non-parametric Statistical Analysis of Diffusion Tensor MRI Data Using the Bootstrap Method. 8th Annual Meeting of the ISMRM, Philadelphia, 1790 (1999).        
Issues about multivariate statistics that are applied to DT-MRI data are discussed in:                (51) T. W. Anderson. An Introduction to Multivariate Statistics: John Wiley & Sons, 1984.        
Computer code implementing algorithms for performing statistical tests are discussed in:                (52) W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery. Numerical Recipes in C. Cambridge: Cambridge University Press, 1992.        
Other clinical and methodological aspects of DT-MRI are provided below:                (53) P. van Gelderen, M. H. M. d. Vleeschouwer, D. DesPres, J. Pekar, P. C. M. v. Zijl, C. T. W. Moonen. Water Diffusion and Acute Stroke. Magnetic Resonance in Medicine 31, 154-163 (1994).        (54) A. M. Ulug, N. Beauchamp, R. N. Bryan, and P. C. M. van Zijl. Absolute Quantitation of Diffusion Constants in Human Stroke. Stroke 28, 483-490 (1997).        (55) M. E. Bastin, M. del Grado, I. R. Whittle, and J. M. Wardlaw. An Investigation into the Effect of Dexamethasone on Intracerebral Tumours using MR Diffusion Tensor Imaging, ISMRM, 902 (1999).        (56) P. Mukherjee, M. M. Bahn, R. C. McKinstry, J. S. Shimony, T. S. Cull, E. Akbudak, A. Z. Snyder, and T. E. Conturo. Differences in Water Diffusion between Gray Matter and White Matter in Stroke: Diffusion Tensor MR Imaging Experience in Twelve Patients. ISMRM, Philadelphia, 73 (1999).        (57) M. A. Horsfield, M. Lai, S. L. Webb, G. J. Barker, P. S. Tofts, R. Turner, P. Rudge, and D. H. Miller. Apparent diffusion coefficients in benign and secondary progressive multiple sclerosis by nuclear magnetic resonance. Magn. Reson. Med. 36 3, 393-400 (1996).        (58) M. A. Horsfield, H. B. Larsson, D. K. Jones, and A. Gass. Diffusion magnetic resonance imaging in multiple sclerosis. J Neurol Neurosurg Psychiatry 64 Suppl 1, S80-84 (1998).        (59) A. O. Nusbaum, C. Y. Tang, M. S. Buchsbaum, L. Shihabuddin, T. C. Wei, and S. W. Atlas. Regional and Global Differences in Cerebral White Matter Diffusion with Alzheimer's Disease. ISMRM, Philadelphia, 956 (1999).        (60) R. Turner, and D. LeBihan. Single shot diffusion imagine at 2.0 Tesla, J Magn. Reson, 86, 445-452 (1990).        (61) J. H. Simpson, and H. Y. Carr. Diffusion and nuclear spin relaxation in water. Physical Review 111 5, 1201-1202 (1958).        (62) H. Y. Carr, and E. M. Purcell. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94 3, 630-638 (1954).        
Techniques for determining the mean ADC are discussed in:                (63) G. Liu, P. van Gelderen, C. T. W. Moonen. Single-Shot Diffusion MRI on a Conventional Clinical Instrument. Second SMR Meeting, San Francisco, 1994, p. 1034.        (64) T. E. Conturo, R. C. McKinstry, E. Akbudak, B. H. Robinson. Encoding of anisotropic diffusion with tetrahedral gradients: a general mathematical diffusion formalism and experimental results. Magn Reson Med 35, 3, 399-412 (1996).        (65) S. Mori, P. C. van Zijl. Diffusion weighting by the trace of the diffusion tensor within a single scan. Magn. Resom. Med. 33, 1, 41-52 (1995).        (66) E. C. Wong, R. W. Cox. Single-shot Imaging with Isotropic Diffusion Weighting. Second Annual Meeting of the SMR, San Francisco, 1994, p. 136.        (67) E. C. Wong, R. W. Cox, A. W. Song. Optimized isotropic diffusion weighting. Magn Reson Med 34, 2, 139-143 (1995).        